Nonfirstorderizability
In formal logic, nonfirstorderizability is the inability of an expression to be adequately captured in particular theories in first-order logic. Nonfirstorderizable sentences are sometimes presented as evidence that first-order logic is not adequate to capture the nuances of meaning in natural language.
The term was coined by George Boolos in his well-known paper "To Be is to Be a Value of a Variable." Boolos argued that such sentences call for second-order symbolization, which can be interpreted as plural quantification over the same domain as first-order quantifiers use, without postulation of distinct "second-order objects".Examples
